Both Sony RX100 and Sony RX10 have 1-inch sized 20.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the RX100 and RX10 sensor size comparison.
Sensor Size and Resolution Comparison image of Sony RX100 and Sony RX10 Cameras
Sony RX100 and Sony RX10 have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture.
DxOMark Sensor Scores
DxOMark is a benchmark that scientifically assesses image quality of camera sensors. It scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Sony RX100 and Sony RX10 sensors have been tested by DxO and the results show that RX10 has a better overall score of 69, 3 points higher compared to RX100's score of 66.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Sony RX100
66
22.6 bits
12.4 Evs
390 ISO
Sony RX10
69
22.9 bits
12.6 Evs
474 ISO
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Sony RX100
or the
Sony RX10 ,
including hyperfocal distance.